On the k-pairs problem

Abstract

We consider network coding rates for directed and undirected $k$-pairs networks. For directed networks, meagerness is known to be an upper bound on network coding rates. We show that network coding rate can be $\Theta (|V|)$ multiplicative factor smaller than meagerness. For the undirected case, we show some progress in the direction of the $k$-pairs conjecture.

ISIT 2008